Research On Unified Calculation Method Of Critical Load And Ultimate Load For Pin-and Fix-end Columns Exhibiting Pure Distortional Buckling

As an efficient method for calculating the distortion critical stress of columns,the Lau and Hancock's formulae has been adopted by China design standard“Technical Standard for Cold-formed Steel Structures"(Approval Draft).However,the Lau and Hancock's formulae are not applicable for calculating the distortional buckling stress for fix-ended columns.In addition,use of the Lau and Hancock's formulae is cumbersome due to too many parameters.The distortional buckling coefficient kD included in the elastic critical distortional buckling stress(?cr,D)formulae,was studied by employing the 5.01 version software CUFSM based on finite strip method.The key scale parameters strongly influenced the coefficient kD were analyzed for C-section with V-stiffer at flange,and the coefficient kD was proposed for pin-and fix-ended columns,respectively.The coefficient kD was then simplified for C-section for pin-and fix-ended columns,respectively.Similarly,the local buckling coefficient kL included in the elastic critical distortional buckling stress(?cr,L)formulae,was studied by CUFSM based on finite strip method in this paper.And the coefficient kL was proposed for C-section with V-stiffer at flange and C-section for pin-and fix-ended columns,respectively.Numerical comparison showed that the complicated calculation was successfully avoided by the proposed formulae,which is applicable for both pin-end C-section columns and fix-ended C-section columns with or without V-stiffener at flange.Most importantly,for C-section included in the China design standard "Technical Standard for Cold-formed Steel Structures"(Approval Draft)and“Cold-Formed Thin-Wall Steel Sections for Building Structures"(JG/T 380—2012),the proposed formulae of elastic critical distortional buckling stress is more accurate than the Lau and Hancock's formulae and the Schafer's formulae.Furthermore,Unified formulae of elastic critical distortional buckling load and unified Direct Strength Method(DSM)expressions for columns undergoing pure distortional buckling,are proposed in this study for both pinned-end and fixed-end columns with a C/Z/hat sections.The normal stress distribution of pre-buckling and post-buckling for C-section columns undergoing distortional buckling is presented based on theoretical analysis and literature review.It is revealed that the basic purpose of the DSM expression is to express the strength problem as a stability problem to determine the ultimate strength of the columns experiencing pure distortional buckling.To understand the effects of both pinned-end and fixed-end conditions in the columns undergoing pure distortional buckling,the effective length factor of flexural buckling about the strong axis of a cross-section,is introduced into elastic distortional buckling load formulae and the DSM expressions.Numerical results computed by CUFSM,along with numerical and experimental results in literature reviews are used to assess the accuracy of the proposed formulae.It is shown that the proposed formulae are accurate and universal.